What is Quantum Tic-Tac-Toe?
Quantum Tic-Tac-Toe uses the usual 3×3 board, X and O, and three in a row to win, but a mark does not go straight into one square. On each turn you place a pair of small spooky marks of your symbol, both labelled with the number of the move, in two different squares. X makes the odd-numbered moves 1, 3, 5, 7 and 9, and O the even ones. The mark will end up in only one of the two squares, but until then it occupies both, and a square can hold spooky marks of several moves at once.
Each pair links its two squares. When a new pair closes a loop of linked squares, for example by putting a mark in the same two squares as an earlier pair, the loop has to collapse. The player who did not close it chooses which of its two squares the newest mark settles in. That square becomes a classical mark, the large ordinary kind, and every other spooky mark in it has to move to its other square, which forces the next mark along, and so on until every mark linked to the loop is classical. The player who chose then makes their own move as usual, so they move twice in a row. Marks that are not linked to the loop stay spooky.
Only classical marks count. The game ends as soon as a collapse leaves a line of three classical marks, or when every square holds a classical mark. If one collapse completes lines for both players, the player whose line was finished earlier wins, measured by the highest move number in each line. When a single square is left, a pair no longer fits, so X's ninth move is an ordinary mark in that square. A full board without a line is a draw.
Rule changes
| Rule | Standard Tic-Tac-Toe | Quantum Tic-Tac-Toe |
|---|---|---|
| Your move | Standard Tic-Tac-ToeWrite your mark in one empty square. | Quantum Tic-Tac-ToePlace two spooky marks of your symbol, labelled with the move number, in two different squares that have no classical mark. A square can hold several spooky marks. |
| Collapse | Standard Tic-Tac-ToeMarks are fixed as soon as they are written. | Quantum Tic-Tac-ToeWhen a pair closes a loop of linked squares, the loop collapses: each mark in it, and every mark linked to it, settles in one square as an ordinary classical mark. |
| Who decides | Standard Tic-Tac-ToeEach player decides only where their own marks go. | Quantum Tic-Tac-ToeThe player who did not close the loop chooses where its newest mark settles, and the rest follows. Then that player makes their own move. |
| How to win | Standard Tic-Tac-ToeComplete a line of three of your marks, across, down or diagonally. | Quantum Tic-Tac-ToeComplete a line of three of your classical marks. Spooky marks never count. |
| Lines for both players | Standard Tic-Tac-ToeImpossible: the game ends at the first line. | Quantum Tic-Tac-ToeOne collapse can complete lines for both players. The line whose highest move number is lower wins. Two lines for one player in one collapse still make one win. |
| End of the game | Standard Tic-Tac-ToeEnds at the first line, or as a draw when the board is full. At most nine marks. | Quantum Tic-Tac-ToeEnds after a collapse that leaves a line, or when the board is full of classical marks. With one square left, X's ninth move is an ordinary mark there. A full board without a line is a draw. |
| Board and options | Standard Tic-Tac-ToeA 3×3 board. The table setup also offers 4×4 and 5×5 boards and the Misère, Wild and gravity rules. | Quantum Tic-Tac-ToeAlways 3×3. Board size, Misère, Wild and gravity are not available with it. |
History
Quantum Tic-Tac-Toe was devised by Allan Goff as a teaching aid for quantum mechanics, and he described it in the American Journal of Physics in 2006. The game is a metaphor rather than a simulation of physics: a mark in two squares at once stands for superposition, marks linked through shared squares for entanglement, and the forced choice when a loop closes for the collapse that happens when a quantum system is measured.
In the published rules a game is scored in points. When one collapse gives both players a line, the player whose line has the lower highest move number scores a full point and the other player half a point. Here the game is played to a single result, so the earlier line wins. Because X's move numbers are odd and O's are even, the two lines can never tie.